Photos of Swift hugging
ArnoldSchwarzenegger's 18-year-old son,
Patrick, over the July 4 holiday set the rumor mill churning that the two were dating. But it was actually Kennedy -- son of
RobertKennedyJr. and the late
MaryKennedy -- with whom she was spending time.

"She is pretty head over heels," the source tells Us.

Swift has previously been linked romantically to celebs like
JakeGyllenhaal,
JohnMayer,
JoeJonas and
TaylorLautner.